I have been working with a document where curves continue to appear in a non-linear way on a variety of objects and attributes. For example, I will create a new text layer, and place position keyframes on it, but the curve will have a strange dip in it that makes it move backwards a bit. I tried recreating another text box and placing it just above, but making the same position adjustments, and the curve dip is the same exact spot. Is something in my document causing everything to have this strange non-linear effect?

You have to read up on how keyframes in AE work. Unless you enabled the "create linear keyframes" option in the preferences, AE will always create Bezier keyframes, with the added difficulty of temporal and spatial interpolation being separate for position keyframes. there's really nothing wrong, you just have to study up on those things instead of making assumptions.

Specifically under "Change interpolation method with the Keyframe Interpolation dialog box." Essentially it appears that to get linear movement in small increments you need to set Spatial Interpolation to linear. Setting "Default Spatial Interpolation to Linear" will set future keyframes to this setting but will not change existing keyframes.